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I introduce world maps with constant scale edges [cse], and show how cse encompasses both conventional projections and a new class of maps—world maps with constant scale natural boundaries [csnb]. Given context this, apparently, strains mathematics, rejoining a “battle” twixt numbers and geometry thought by some, perhaps, long-settled in favor of algebra. Here geometry betters its cousin, as when numbers, shy the idea of an irrational number, once lost the number-line’s challenge. The idea of “natural boundary” mapping is simple, and in principle offers substantial advantage for studying natural, globular objects—dynamic and spherical planets like Earth and Venus, and odder things like Eros and Ios. But, such maps are difficult to make, and heretofore suffered the usual drawbacks of maps in general, e.g. distorted periphery and unintelligible edge. Computers would end the tedium of plotting points; and constant scale joined to natural boundary re-imagines maps.